Binary boundary codes

Over the years several numerical codes have been developed for benzenoids, such as the boundary code (Trinajstic et al. 1983 von Knop et al. 1983), the DAST code (Miiller et al. 1990), but the binary boundary code (Trinajstic et al. 1983 Herndon and Bruce 1987 Klein et al. 1988) appears to be the simplest to use. 

Among the five possible binary botmdary codes of the naphthalene-bihex, the maximum code is selected 1111011110. The binary boundary code is unique since two non-isomorphic polyhexes cannot produce the same code. In Fig. 9.8, we give the binary botmdary code for the given orientation of the dibenzo[I>,g] phenanthrene polyhex. A mirror-image orientation of the dibenzo[f>,g]phenan-threne polyhex produces the maximum binary boundary code for this structure 1111011011010111101000. 

A way to recover a given polyhex from its binary boundary code is shown in Fig. 9.9. 

Fig. 9.7 A bihex representing the carbon skeleton of naphthalene and its five possible binary boundary codes...

Fig. 9.8 The binary boundary code for a given orientation of the dibenzo[i>, glphenanthrene polyhex...

Fig. 9.9 Recovery of dibenzo[e,m]peropyrene from the corresponding hinary houndary code (a) Binary boundary code 11110101100011110011101100110 0, (b) Construction of the polyhex houndary from the given hinary houndary code, (c) Construction of the polyhex hy filling in the inner space restricted hy the boundary, (d) Recovered polyhex...

If the detection process is publicly known, an attacker can perturb the public signal s in such a way that the attacked signal r exactly lies on the decision boundary between different quantizer points. For binary dither modulation these points are depicted by the short lines in Fig. 3 (left). After such an attack, the decoder can only randomly guess whether the received signal sample was originally quantized by Qo or Qi. Thus, the watermark information is completely lost. Note that no chaimel coding can help to recover information from the such attacked signal. 

---